Despite insubstantial but influential claims from the early days of quantum theory, Bohm proved in 1952 [1]} that it is possible to give a straightforward realist interpretation of quantum mechanics with particles in space-time. However, in that theory the underlying dynamics occurs in higher-dimensional configuration space, resulting in explicitly nonlocal dynamics in space-time. In this article we lay out the general framework for local realist collapse-free theory quantum mechanics, and work through the simplest examples, with all dynamics occurring explicitly in space-time. This realizes an unachieved goal of Einstein, Schrödinger, and Lorentz, who were never satisfied with the configuration space treatment, precisely because it introduced fundamental nonlocality [2]}. The new model makes identical empirical predictions to standard quantum theory, and can serve as a full replacement. This model is consistent with the Lorentz covariant Heisenberg-Schrödinger model proposed by Schwinger in 1948 [3]}, and restores the equivalence between the local Heisenberg and Schrödinger pictures. However, we now know from Bell's theorem [4]}, [5]}, [6]}, [7]}, [8]} that if we wish to maintain independence of measurement settings, then this is unavoidably a theory of many local worlds [9]}.
